Calcul algébrique : Test de niveau 2

Calculez \(\left( \dfrac{1}{2}+\dfrac{6}{7}-\dfrac{1}{14}\right) \cdot \left( \dfrac{2}{3}-\dfrac{3}{4}\right)\).

Calculez \(\left(\dfrac{1}{x}+\dfrac{1}{y}\right)/\left(\dfrac{1}{x^2}-\dfrac{1}{y^2}\right)\).

Si \(a=0,2\), \(b=-0,1\) et  \(c=-0,5\), calculez \((\frac{a}{b}+\frac{b}{c})\cdot \frac{c}{a}\).

Calculez \(\dfrac{3x+3y}{x^2-y^2}+\dfrac{7x-7y}{x^2-2xy+y^2}\).

L'expression \(\dfrac{2/3+3/4}{5/6-7/8}\) vaut

Ecrivez l'expression \(\displaystyle{\frac{1}{5\sqrt[3]{25}}}\) sous forme de puissance.

Calculez \(\dfrac{\sqrt{6}}{2\sqrt{3}-5\sqrt{2}}\).

Calculez \(\left(\dfrac{5}{16}\left(\dfrac{3}{10}+\dfrac{1}{2}\right)-\dfrac{1}{8}\right)\left(-\dfrac{5}{2}\right)\).

Simplifiez la fraction \(\dfrac{3x^2-xy}{6xy-2y^2}\).

Calculez \(\left(\dfrac{x-y}{x+y}\right)/\left(\dfrac{x^2-y^2}{x^2+2xy+y^2}\right)\).